Polarimeters and ellipsometers are comprised of optical elements such as polarizer and retarder systems. Polarimeter systems allow the polarization state of a polarized beam of electromagnetic radiation to be determined, and ellipsometer systems allow detection of change in polarization state of a polarized beam of electromagnetic radiation resulting from interaction with a sample system to be determined, said change in polarization state being associated with optical and physical properties of said sample system. For general information it is noted that the polarization state of a polarized beam of electromagnetic radiation is determined by:
a. ratio of orthogonal components, (related to PSI); PA1 b. phase angle between said orthogonal components, (related to DELTA); PA1 c. absolute value of one orthogonal component; and PA1 d. the direction of rotation, or handedness. PA1 translational; and PA1 rotational; PA1 a source of electromagnetic radiation; PA1 a polarizer system; PA1 a compensator/retarder; PA1 an analyzer; and PA1 a detector system. PA1 a. providing a spectroscopic ellipsometer/polarimeter system sequentially comprising: PA1 b. placing a sample system into said spectroscopic ellipsometer/polarimeter system; PA1 c. causing said source of electromagnetic radiation to provide a beam of electromagnetic radiation to said sample system; and PA1 d. detecting said beam of electromagentic radiation after interaction thereof with said sample system. PA1 translational; and PA1 rotational; PA1 a. providing a present invention Spectroscopic Rotating Compensator Material System Investigation System as just described infra herein. PA1 b. developing a Mathematical Model of said Spectroscopic Rotating Compensator Material System Investigation System which comprises as Calibration Parameter variables Polarizer Azimuthal Angle Orientation, present Material System PSI, present Material System DELTA, Compensator Azimuthal Angle Orientation(s), Matrix Components of said Compensator(s), Analyzer Azimuthal Angle Orientation, and optionally Detector Element Image Persistance and Readout non-idealities, which Mathematical Model is effectively a Transfer Function which enables calculation of Electromagnetic Beam Intensity as a function of Wavelength detected by a Detector Element, given Intensity as a function of wavelength provided by said Source of a Polychromatic Beam of Electromagnetic Radiation, said Mathematical Model optionally providing equations for Coefficients of Terms in said Transfer Function, said Coefficients of terms being functions of Calibration Parameters; PA1 c. causing a Polychromatic Beam of Electromagnetic Radiation produced by said Source of a Polychromatic Beam of Electromagnetic Radiation, to pass through said Polarizer, interact with a Material System caused to be in the path thereof, pass through said Analyzer, and interact with said Dispersive Optics such that a Multiplicity of Essentially Single Wavelengths are caused to simultaneously enter a corresponding Multiplicity of Detector Elements in said at least one Detector System, with said Polychromatic Beam of Electromagnetic Radiation also being caused to pass through said Compensator(s) positioned at a location selected from the group consisting of: (before said Stage for Supporting a Material System and after said Stage for Supporting a Material system and both before and after said Stage for Supporting a Sample System); PA1 d. obtaining an at least Two Dimensional Data Set of Intensity Values vs. Wavelength and a parameter selected from the group consisting of: (Angle-Of-Incidence of said Polychromatic Beam of Electromagnetic Radiation with respect to a present Material System, and Azimuthal Angle Rotation of one element selected from the group consisting of: (said Polarizer and said Analyzer)), over time, while at least one of said at least one Compensator(s) is caused to continuously rotate and, optionally, from said data set calculating numerical values for Coefficients of Terms in the Transfer Function for said Spectroscopic Rotating Compensator Material System Investigation System; PA1 e. performing a Mathematical Regression of said Mathematical Model onto said at least Two Dimensional Data Set and/or onto values for Coefficients of Terms in the Transfer Function to evaluate said Calibration Parameters; PA1 A Polychromatic Light Source PA1 A Fixed Polarizer PA1 A Material Sample PA1 A Continuously Rotating Compensator PA1 A Fixed AnalyzeR, and PA1 A Detector Element containing Photo Array. PA1 P is the azimuthal orientation of the Polarizer; PA1 C is the azimuthal orientation of the Rotating Compensator; PA1 r1, r2, r3 & r4 are the Jones Matrix elements which describe the Compensator, (Note that a Jones Matrix is utilized, however, a Mueller Matrix or other Matrix could also be utilized); PA1 A is the azimuthal orientation of the Analyzer. PA1 r1=1; PA1 r2=0; PA1 r3=0; and PA1 r4=e.sup.i-.delta. ; PA1 1. It accurately represents the behavior of the Calibration Parameter at each Independent Variable (eg. Photo Array Channel or Wavelength). PA1 2. It accurately represents the behavior of the Calibration Parameter utilizing fewer Parameters than would be required to simply evaluate Calibration Parameters at each utilized Independent Variable (eg. Wavelength).
It is noted that an ideal polarizer would pass only linearly polarized electromagnetic radiation aligned with the fast axis thereof, and would reject all electromagnetic radiation in an orthogonal orientation. That is, the extinction ration would be essentially infinite. The Mueller Matrix for an ideal polarizer is provided below: ##EQU1##
An ideal Retarder system would enter a phase retardation between orthogonal components of polarized electromagnetic radiation without preferentially modifying the intensity of either orthogonal component thereof. The Mueller Matrix of an ideal Retarder is: ##EQU2## where "r" is the entered retardence.
As even very good compensator/retarder systems tend to preferentially modify one orthogonal component of an electromagnetic beam of radiation, (including those presented in this Disclosure), it is necessary to modify said Mueller Matrix to account for said effect. The Mueller Matrix of a Retarder system which accounts for preferential modification of one orthogonal component of a polarized beam of electromagnetic radiation is: ##EQU3## where "r" is again the retardence entered. Note that where Retarder system PSI (.PSI.) is forty-five (45) degrees, said Mueller Matrix reduces to the ideal Mueller Matrix.
It is additionally noted that the value of "r" should be in a range where an ellipsometer system in which it is a component is not severely sensitive to changes therein as, for instance, a function of wavelength. In Rotating Compensator Ellipsometers, it is disclosed that a value of "r" between ninety (90) and one-hundred-fifty (150) degrees is generally acceptable. It is also noted that typical off-the-shelf Retarder systems often exhibit an "r" with a (1/wavelength) response such that "r" values are not within said 90 to 150 degree range, when observed over a wavelength range of say, two-hundred-fifty (250) to one-thousand (1000) nm.
It is a requirement of an ideal optical element that a beam of electromagnetic radiation caused to interact therewith not have its direction of propagation deviated or displaced thereby. This is especially critical where an optical element must be rotated in use.
It is further desirable that an optical element not exhibit sensitivity of, for instance, extinction ratio, or retardence entered between orthogonal components of an electromagnetic beam of radiation caused to interact therewith, as a function of beam alignment with respect thereto.
As well, it is desirable that optical elements be easy to fabricate and that fabrication be from easily obtainable materials.
Continuing, the practice of ellipsometry requires that data reflecting change in polarization state of an electromagnetic beam of radiation resulting from interaction with a sample system be obtained and that said data be compared to data generated by use of a proposed mathematical model. Said mathematical model must take into account all nonidealities of optical elements present in the ellipsometer utilized. It is thus preferable to have as few nonidealities present in optical elements as is possible, in order to simplify mathematical model complexity.
With an eye to the present invention, a Search of Patents was conducted. Said Search was focused on polarizers, and on compensator/retarder systems which might provide relatively stable retardation over a range of wavelengths without imposing deviation or displacement in a beam of electromagnetic radiation caused to pass therethrough.
Regarding compensator/retarder systems, Patents were found which show elements with geometry somehow similar to geometry of the present invention compensator/retarder systems, but the present invention use was not found. In particular, attention is directed to the Figure in U.S. Pat. No. 548,495 to Abbe; FIG. 2 in U.S. Pat. No. 4,556,292 to Mathyssek et al.; FIGS. 1 & 4 in U.S. Pat. No. 5,475,525 Tournois et al.; and FIG. 10 in U.S. Pat. No. 5,016,980 Waldron. U.S. Pat. No. 3,817,624 to Martin and U.S. Pat. No. 2,447,828 to West were also identified.
Additional searching of Patents identified Dill U.S. Pat. No. 4,053,232 which describes a Rotating-Compensator Ellipsometer System, which operates utilizes monochromatic light. Two Patents which identify systems which utilize Polychromatic light in investigation of material systems are described in U.S. Pat. Nos. 5,596,406 and 4,668,086, to Rosencwaig et al. and Redner, respectively, were also identified. Also identified Woollam et al, U.S. Pat. No. 5,373,359 as it describes a Rotating Analyzer Ellipsometer System which utilizes white light. Patents continued from the 359 Woollam et al. U.S. Pat. Nos. 5,504,582 to Johs et al. and 5,521,706 to Green et al. Said 582 Johs et al. and 706 Green et al. Patents describe use of polychromatic light in a Rotating Analyzer Ellipsometer System. Bernoux et al., U.S. Pat. No. 5,329,357 is identified as it describes an ellipsometer system in which polarizer rotation is caused during use. Chen et al., U.S. Pat. No. 5,581,350 is identified as it describes the application of regression in calibration of ellipsometer systems. An article by Johs, titled "Regression Calibration Method For Rotating Element Ellipsometers", which appeared in Thin Film Solids, Vol. 234 in 1993 is also identified as it predates the Chen et al. Patent and describes an essentially similar approach to ellipsometer calibration. An article by Jellison Jr. titled "Data Analysis for Spectroscopic Ellipsometry", Thin Film Solids, 234, (1993) is idnetified as it describes a method of determining the accuracy with which certain data points can be measured, which information allows adding a weighting factor to a curve fitting regression procedure as applied to a multiplicity of data points, said weighting factor serving to emphasize the effect of more accurate and precise data. A book by Azzam and Bashara titled "Ellipsometry and Polarized light" North-Holland, 1977 is disclosed and incorporated herein by reference for general theory. An article by Collins titled "Automated Rotating Element Ellipsometers: Calibration, Operation, and Real-Time Applications", Rev. Sci. Instrum. 61(8), August 1990 is identified as it provides insight into rotating element ellipsometers. An article by Kleim et al. titled "Systematic Errors in Rotating-Compensator Ellipsometry" published in J. Opt. Soc. Am./Vol. 11, No. 9, September 1994 is identified as it describes calibration of rotating compensator ellipsometers. An Article by An and Collins titled "Waveform Analysis With Optical Multichannel Detectors: Applications for Rapid-Scan Spectroscopic Ellipsometer", Rev. Sci. Instrum., 62 (8), August 1991 is also identified as it discusses effects such as Detection System Error Characterization, Stray Light, Image Persistence etc., and calibration thereof. Also disclosed are articles by Schubert et al. which describe "Generalized Ellipsometry". The first thereof is titled "Extension Of Rotating-Analyzer Ellipsometry To Generalized Ellipsometry: Determination Of The Dielectric Function Tensor From Uniaxial TiO2", J. Opt. Soc. Am. A. 13, (1996). The second such article is authored by M. Schubert alone and is titled "Polarization Dependent Parameters Of Arbitrary Anisotropic Homogeneous Epitaxial Systems", Phys. Rev. B 53, (1996). The third such article is titled "Generalized Transmission Ellipsometry For Twisted Biaxial Dielectric Media: Application To Chiral Liquid Crystals", J. Opt. Soc. Am. A/Vol. 13, No. 9 (1996). Further identified for authority regarding regression is a book titled Numerical Recipes in "C", 1988, Cambridge University Press.
A compensator/retarder system which can be configured so that it introduces essentially no deviation or displacement into a beam of electromagentic radiation caused to interact therewith, it should then be appreciated, would provide utility. The present invention provides an optical compensator/retarder system which demonstrates acceptably ideal behavior over relatively large wavelength ranges, and which can be applied to usage in rotating compensator ellipsometer systems.